uva 12470

矩陣+快速幂模

//====================================================================||
//                                                                    ||
//                                                                    ||
//                         Author : GCA                               ||
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||
//====================================================================||
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
using namespace std;
#ifdef ONLINE_JUDGE
#define ll "%lld"
#else
#define ll "%I64d"
#endif
typedef unsigned int uint;
typedef long long int Int;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\n")
#define I_de(x,n)for(int i=0;i<n;i++)printf("%d ",x[i]);Pln()
#define De(x)printf(#x"%d\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\
    printf("%d ",dp[htx][hty]);}Pln();}
#define M 55
#define PII pair<int,int>
#define PB push_back
#define oo INT_MAX
#define Set_oo 0x3f
#define Is_debug true
#define debug(...) if(Is_debug)printf("DEBUG: "),printf(__VA_ARGS__)
#define FOR(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++)
#define eps 1e-6
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
int min3(int x,int y,int z){
    int tmp=min(x,y);
    return min(tmp,z);
}
int max3(int x,int y,int z){
    int tmp=max(x,y);
    return max(tmp,z);
}
Int n;
Int mod=1000000009;
struct m{
    Int x[3][3];
    m(){
        Set(x,0);
    }
}a;

m mul(m a,m b){
    m ans;
    for(int i=0;i<3;i++){
        for(int j=0;j<3;j++){
            ans.x[j][i]=(a.x[0][i]*b.x[j][0])%mod;
            ans.x[j][i]=(ans.x[j][i]+a.x[1][i]*b.x[j][1])%mod;
            ans.x[j][i]=(ans.x[j][i]+a.x[2][i]*b.x[j][2])%mod;
        }
    }
    return ans;
}
void pm(){
    m ans;
    for(int i=0;i<3;i++)
        for(int j=0;j<3;j++)
            if(i==j)ans.x[i][j]=1;
    while(n>0){
        if(n&1)
            ans=mul(ans,a);
        a=mul(a,a);
        n>>=1;
    }
    Int fans=(2*ans.x[0][0])%mod;
    fans=(fans+ans.x[1][0])%mod;
    printf("%lld\n",fans);
}
int main() {
    ios_base::sync_with_stdio(0);
    while(~scanf("%lld",&n)&&n){

        Set(a.x,0);
        a.x[0][0]=a.x[1][0]=a.x[2][0]=a.x[0][1]=a.x[1][2]=1;
        if(n<=3){
            printf("%lld\n",n-1);
        }else{
            n-=3;
            pm();
        }
    }

















}